It probably doesn't hold up. The idea of overpopulation is wrong because the west is suffering a birth crisis while the third world is having a child boom. It's not that more children are being born, it's that their standards are being improved so more of them survive. They in turn will level out and see less children born the better their standards become; so it's reasonable to assume if standards are collapsing in the west, then in a generation or so, more children will be born.